Large-scale discrete data analysis of various scientific computational simulations often requires high-order continuous functional representations that have to be evaluated anywhere in the domain. Such expansions described as Multivariate Functional Approximations (MFA) [1]}, [2]} in arbitrary dimensions allow the original discrete data to be compressed, and expressed in a compact form, in addition to supporting higher-order derivative queries (without further approximations such as finite differences) for complex data analysis tasks. MFA utilizes approximations of the raw discrete data using a hypervolume of piecewise continuous functions. One particular option is to use the variations of the B-Spline or NURBS bases [3]}, [4]} for the MFA encoding of scientific data. The reconstructed data in MFA retains the spatiotemporal contiguity, and statistical distributions, with lesser storage requirements. Due to the potentially large datasets that need to be encoded into MFA, the need for computationally efficient algorithms (in both time and memory) to parallelize the work is critically important. It is also essential to guarantee that the solution smoothness in the reconstructed (or decoded) dataset is consistently preserved when transitioning from a single MFA domain to multiple domains during parallelization.
